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Answers
Answer: Hey! Here's your answer.
Step-by-step explanation:
Given : Square ABCD and equilateral triangle EAB.
To prove: (i) Angle DAE = Angle CBE = 30°
(ii) Triangle ADE is congruent to Triangle BCE.
(i) As given in the figure, Square ABCD and Triangle EAB share the same base.
WKT, Angle DAB = 90° (All interior angles of a square measure 90°)
We also know that, Angle EAB = 60° ( since Triangle EAB is equilateral)
Therefore, Angle DAE = 90° - 60° = 30°
Similarly, Angle CBE = Angle CBA - Angle EBA = 90° - 60° = 30°
Hence, Angle DAE = Angle CBE = 30°
(ii) In Triangles ADE & BCE,
Angle DAE = Angle CBE (previously proven)
AD = BC (since all sides of a square are equal in length)
EA = EB (since EAB is an equilateral triangle)
Therefore, by SAS congruence criterion, Traingle ADE is congruent to Triangle BCE.
Hence, proven.
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